NASA Technical Reports Server (NTRS) 20000063501: Cumulative Axial and Torsional Fatigue: An Investigation of Load-Type Sequencing Effects

48 Pages·1.2 MB·English

by  NASA Technical Reports Server (NTRS)

TITLE OF SYMPOSIUM: MultiaxialFatigueandDeformation:TestingandPrediction
AUTHORS' NAMES:
Sreeramesh Kallud ! and Peter J. Bonacuse 2
TITLE OF PAPER:
Cumulative Axial and Torsional Fatigue: An Investigation of Load-Type Sequencing Effects
(Paper ID # 8013)
AUTHORS' AFFILIATIONS:
1Senior Research Engineer, Ohio Aerospace Institute, NASA Glenn Research Center, Cleveland,
Ohio.
2Materials Research Engineer, Army Research Laboratory, NASA Glenn Research Center,
Cleveland, Ohio.
Thisisa preprint or reprint of apaper intended for presentation ata conference.
Because changes may be made before formal publication, this ismade available with the
understanding that itwill not be cited or reproduced without thepermission ofthe author.
ABSTRACT: Cumulative fatigue behavior of a wrought cobalt-base superalloy, Haynes 188
was investigated at 538°C under various single-step sequences of axial and torsional loading
conditions. Initially, fully-reversed, axial and torsional fatigue tests were conducted under strain
control at 538°C on thin-walled tubular specimens to establish baseline fatigue life relationships.
Subsequently, four sequences (axial/axial, torsional/torsional, axial/torsional, and torsional/axial)
of two load-level fatigue tests were conducted to characterize both the load-order (high/low) and
load-type sequencing effects. For the two load-level tests, summations of life fractions and the
remaining fatigue lives at the second load-level were computed by the Miner's Linear Damage
Rule (LDR) and a nonlinear Damage Curve Approach (DCA). In general, for all four cases
predictions by LDR were unconservative. Predictions by the DCA were within a factor of two of
the experimentally observed fatigue lives for a majority of the cumulative axial and torsional
fatigue tests.
KEYWORDS: axial fatigue, cumulative fatigue, cyclic hardening, damage curve approach, life
prediction, linear damage rule, load-type sequencing, torsional fatigue
Nomenclature
b, c Exponents of elastic and inelastic strain range-life relations
n Number of applied cycles at a load level in a cumulative fatigue test
B,C Coefficients of elastic and inelastic strain range-life relations
MF Multiaxiality factor
N Number of cycles
TF Triaxiality factor
E Engineering axial strain
7 Engineering shear strain
V Frequency of the waveform in a fatigue test
A Denotes range of a variable
t_ Axial stress
Shear stress
Subscripts
1 First load level in a two-load level cumulative fatigue test
2 Second load level in a two-load level cumulative fatigue test
el elastic
in inelastic
m mean value
f failure
A Axial
T Torsional
I First principal
II Second principal
III Third principal
Introduction
Accumulation of damage in materials subjected to fatigue under multiple load levels and
estimation of cyclic life under cumulative fatigue has been the subject of investigation for the
past 75 years [1-13]. In these cumulative fatigue investigations materials have been typically
subjected to the same load-type (for example, axial tension/compression [3,13], torsion [4,8,9],
orrotatingbending[5,6]),albeittodifferentmagnitudesd,uringthemultipleloadinglevels.In
engineeringdesign,fatiguelife undercumulativefatigueloadingconditionsiscommonly
estimatedwithaLinearDamageRule (LDR) [1-3],primarilyduetoitssimplicity,associated
easeof implementationa,ndlackofprovenapplicabilityofalternativerules.However,
inadequacyoftheLDRtoproperlyaccountfortheloadordereffects(eitherhigh/loworlow/high
foragivenload-type)hasbeenwell documentedintheliterature [6-13]. Withinaspecified
load-type,thehigh/lowloadorderingtypicallygeneratesa sum of life fractions less than unity,
whereas the low/high load ordering typically generates a sum of life fractions greater than unity.
Several nonlinear damage accumulation models [6-12] have been developed to overcome the
disadvantages of the LDR for predicting fatigue lives of materials subjected to multiple load
levels. Most of the nonlinear damage accumulation models capture the well-known load order
effects adequately for a given load-type under cumulative cyclic loading conditions.
The cumulative fatigue behavior of materials under dissimilar load-types could
potentially be different from that under a single load-type due to either a lack of interaction or a
potential synergistic interaction between the deformation and damage modes and their
orientation associated with the two load-types. Investigations involving cumulative fatigue of
materials with dissimilar load-types are relatively recent in comparison to those involving the
same load-type [14-22]. During the past 15-20 years, researchers have investigated accumulation
of fatigue damage in materials under dissimilar load-types such as 1) tension/compression,
torsion, and proportional and nonproportional combined axial-torsional loads [14-17, 19-22] and
2) torsion and bending [18]. For cumulative fatigue involving axial and torsional loading
conditions most of the previous studies have been conducted with 1) the same equivalent strain
range [14,17,19,20], 2) the same fatigue lives [16], or 3) with the same equivalent damage [21].
Equivalencyintermsofstrainrange,fatiguelife, ordamageisselectedprimarilytoseparatethe
loadordereffectsfromtheload-typesequencingeffects.Ingeneralu, nderequivalentloading
conditions,cyclictension/compressiofnollowedbycyclictorsiontypeloadsequencinghasbeen
foundtobemorebenignthanthatpredictedbyLDR(forexample,withasumofcyclefractions
greaterthanunity),whereastheload-typesequencingofcyclictorsionfollowedbycyclic
tension/compressiohnasbeenreportedtobemoredamagingtharithatestimatedbyLDR (witha
sumofcyclefractionslessthanorequaltounity) [16,17,19,20].However,in afew
investigations[19-21] ithasbeenreportedthattheload-typesequencingofcyclic
tension/compressiofnollowedbycyclictorsionismoredetrimentalthancyclictorsionfollowed
bycyclictension/compressionT.hisreversailn load-typesequencingeffectshasbeenattributed
todifferencesinthecrackingpatternsofmaterialsthatarecausedbytemperaturedependent
environmentaleffects(forexample,oxidation)andinherentdifferencesin microstructures.
Cumulativefatigueinvestigationsthatconsideredloadorderaswellasload-typesequencing
effectsundercyclicaxialandtorsionalloadsareratherlimitedinnumber[15,22].Asfaras
fatiguelife estimationisconcernedn,oticeabledeviationsfromtheLDRhavebeenreportedin
bothstudies.
Theobjectiveofthepresentstudywastoevaluatetheeffectsofbothload-type
sequencingandhigh/lowloadorderingundercumulativeaxialandtorsionalloadingconditions.
Atestprogramwasdesignedtoinvestigatethecumulativefatiguebehaviorofarepresentative
hightemperaturesuperalloyundervarioussequenceosfaxialandtorsionalloadingconditions.
Thewroughtcobalt-basesuperalloy,Haynes188wasselectedforthispurpose.Examplesofthe
manyapplicationsofthissuperalloyincludethecryogenicoxygencarryingtubesinthemain
injectorofthereusablespaceshuttlemainengineandthecombustorlinerintheT-800turboshatt
enginefortheRAH-66Comanchehelicopter.Axial,torsional,andcombinedaxial-torsional
fatiguebehaviorofHaynes188underisothermal(316and760°C)andthermomechanica(l316to
760°C)loadingconditionsonasingleheatofthesuperalloywaspreviouslydocumentedbythe
authors[23-27]. Inthecurrentinvestigation,axialandtorsionalfatiguetestswereconductedat
538°ConmaterialfromanotherheatofHaynes188toestablishbaselinefatiguelives.
Subsequentlyfoursequence(saxial/axial,torsional/torsionala,xial/torsional,andtorsional/axial)
oftwoload-level(single-step)fatiguetestswereconducted(sameheatasthatusedforthe
baselinetests)at538°Ctocharacterizethecumulativefatiguebehaviorofthesuperalloy.Forthe
two load-leveltests,summationsoflife fractionsandtheremainingfatiguelivesatthesecond
load-levelwereestimatedwithtwomodels,LDR[1-3]andthenonlinearDamageCurve
Approach(DCA) [7,10]. This paper summarizes details of the test program, results from the
axial and torsional cumulative fatigue tests, and predictive capabilities of the models.
Material and Specimens
Solution annealed, hot rolled, cobalt-base superalloy, Haynes 188, was supplied by the
manufacturer in the form of round bars with a diameter of 50.8 mm (heat number: 1-1880-6-
1714). The composition of the superalloy in weight percent was as follows: <0.002 S, 0.003 B,
<0.005 P, 0.09 C, 0.35 Si, 0.052 La, 0.8 Mn, 1.17 Fe, 14.06 W, 22.11 Cr, 22.66 Ni, balance Co.
Thin-walled tubular specimens with nominal inner and outer diameters of 22 and 26 mm,
respectively, in the straight section (41mm) and an overall length of 229 mm were machined
from the bar stock. Bores of the tubular specimens were finished with a honing operation and the
external surfaces of the specimens were polished. Additional details on machining of tubular
specimens are available in Ref. [28]. In the middle of the straight section of the tubular
speciment,wo indentations(25mmapartand80lamdeep)werepressedwith afixturetodefine
thegaugesectionandtopositivelylocatetheextensometeprrobes.Averagevaluesoftheelastic
modulus,shearmodulus,andpoisson'sratioforHaynes188at538°Cwere190GPa,73GPa,
and0.3respectively.
Experimental Details
All the tests were performed in an axial-torsional fatigue test system [27] equipped with a
personal computer and a data acquisition system. Tubular specimens were heated to the test
temperature of 538°C in air with a three-coil fixture [29] connected to a 15 kW induction heating
unit. Specimen temperature in the gauge section was measured with a noncontacting optical
temperature measurement device. Thermocouples spot-welded in the shoulder regions of the
specimens were used to control and monitor the temperature during fatigue tests. Axial and
engineering shear strains within the gauge section of each specimen were measured with a water-
cooled, axial-torsional extensometer. Test control soft-ware written in C language was used to
generate triangular, axial and torsional command waveforms at the appropriate frequencies for
the strain-controlled fatigue tests. For each axial and torsional fatigue test, test control software
increased the strain to the full amplitude by increasing the strain increments linearly over 10
cycles. For axial strain-controlled fatigue tests, the torsional servocontroller was in load-control
at zero torque and for torsional strain-controlled fatigue tests, the axial servocontroUer was in
load-control at zero load. In the case of cumulative fatigue tests with two load-levels, after
completing the required number of cycles at the first load-level, test control software decreased
the strain amplitude to zero by reducing the strain increments linearly over 10 cycles. This
procedure was necessary to return the material to an approximately zero stress and zero strain
stateinacarefullycontrolledmanner.Softwarewasalsousedtoacquireaxialandtorsionalload,
strain,andstrokedataatlogarithmicintervalsin cyclesandtoshutdowneachtestin acontrolled
manner.Foraxialandtorsionalfatiguetests,failurewasdefinedasa10%load-dropfroma
previouslyrecordedcycle. If aspecimendidnotfail after250,000cycles,thenthattestwas
declaredarunout.
Results
Baseline Axial and Torsional Fatigue Tests
Fully reversed, strain-controlled, axial and torsional fatigue tests were conducted at
538°C to establish baseline fatigue data for the subsequent cumulative fatigue tests. Axial and
torsional fatigue data obtained from near half-life cycles are listed in Tables 1 and 2,
respectively. For both axial and torsional tests at higher strain ranges a frequency of 0.1 Hz was
used, whereas at lower strain ranges a frequency of 0.5 Hz was used. Lowering of the frequency
at higher strain ranges was necessary to achieve adequate control of the fatigue test in the
presence of 'serrated yielding' [30] exhibited by Haynes 188 at 538°C [31]. Slight compressive
mean stresses were observed in all the axial fatigue tests, whereas no appreciable mean stresses
were noticed in the torsional fatigue tests. In a majority of the torsional fatigue tests, axial strain
ratchetting in the positive direction was observed. Such axial strain ratchetting in materials
subjected to torsional loading was reported by other investigators [32-35] and was also observed
in Haynes 188 at 760°C [36]. However, for the tests conducted in the present study, magnitudes
of the mean axial ratchetting strains near half-lives were either less than or of the same order as
the equivalent imposed engineering shear strains. In a separate study [37] also conducted on
Haynes 188 no significant influence of mean axial strain, either tensile or compressive, was
observed on the axial fatigue life of the superalloy.
9
Inthebaselinetests,orientationofthecrack(s)thatleadtospecimenfailurewasnearly
perpendiculartothemaximumnormalstressintheaxialfatiguetests,whereasinthetorsional
fatigueteststhecrackorientationwasalwaysparalleltooneofthetwomaximumshear
directions(Tables1and2).Axial andtorsionalfatiguelife relations(Eqs.1and2)were
computedbyseparatingthetotalstrainrangeforeachtestintoelasticandinelasticcomponents
(Tables1and2),andsubsequentlyperformingaregressionbsetweenlogarithmsofthestrain
rangecomponentsandthefatiguelives.Fatiguedatafromthertmouttestswereomittedwhile
computingthelife relationships.Constantsfortheaxialandtorsionallife relationshipsareshown
inTable3.
fEq.i)
Ae = B(Nf) b+ C(Nf) _
(Eq. 2)
A? = BT(N,) b' + CT(N,) "
Axial and torsional fatigue data and the corresponding life relationships are plotted in Figs. 1 and
2, respectively. Note that for Haynes 188 at 538°C, the slopes of the elastic and inelastic life
relations for the axial and torsional loading conditions are very similar. Axial and torsional
fatigue data are compared by using von Mises equivalent strain range (Aeeq= A?/_/3) in Fig. 3.
Most of the torsional fatigue data fall near the axial fatigue curve. The torsional fatigue life
relationship was estimated from the axial fatigue life relationship by the Modified Multiaxiality
Factor (MMF) Approach (Eqs. 3 and 4).
(Eq. 3)
l0
where,
(Eq. 4)
MF = TF; TF > 1
TF= O"I 4- _II "1- CYIII
_/((Yl -- O'II) 2 + ((3"Ii -- (YlII) 2 "_"(Oill --0"1 )2
This approach was previously used to estimate torsional fatigue behavior from axial fatigue life
relationships of Haynes 188 at 316 and 760°C [24,25]. For torsion (erI = - crmand on = 0; TF = 0;
and MF = 0.5), the estimated torsional fatigue life relation from Eqs. 3 and 4 forms an upper
bound to the experimentally observed torsional fatigue data at 538°C (Fig. 3).
Four nominal strain ranges, two each for axial (A_ 1= 0.02 & A_ 2= 0.0067) and torsional
(Ay_ = 0.035 & AY2= 0.012) loading conditions, were selected for the subsequent cumulative
fatigue tests. Duplicate tests were conducted in the baseline test program to evaluate
repeatability of the cyclic deformation behavior and to provide a more accurate estimate of the
fatigue life for each test condition. The evolution of cyclic axial and shear stresses are plotted in
Fig. 4 for the baseline axial and torsional tests. In each of these tests, Haynes 188 exhibited
cyclic hardening for a majority of the life with a slight softening towards the end of the test. No
significant differences were observed between the cyclic hardening behaviors of the duplicate
tests. For a given cyclic loading condition, scatter in fatigue life typically exhibits a log-normal
distribution. Therefore, geometric mean lives (arithmetic means of the logarithms of fatigue
lives) of the duplicated axial and torsional baseline fatigue tests were used to design the